Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Wolfgang Beyer
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        MaximumAverageSets solver = new MaximumAverageSets();
        solver.solve(1, in, out);
        out.close();
    }

    static class MaximumAverageSets {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();
            long[] v = in.readLongArray(n);
            Arrays.sort(v);

        /*if (v[n - a] == v[n - 1]) {
            out.println(v[n - 1]);
            int total = a;
            while ((total < n) && (v[n - total - 1] == v[n - 1])) {
                total++;
            }
            long result = 0;
            for (int i = a; i < Math.min(total, b); i++) {
                result += choose(total, i);
            }
            out.println(result);
            return;
        }*/

            long sum = 0;
            for (int i = n - 1; i >= n - a; i--) {
                sum += v[i];
            }
            double av = (double) sum / a;
            //out.println((double) sum / a);
            out.format("%.6f\n", av);

            int selectMin = 1;
            while ((selectMin < a) && (v[n - a + selectMin] == v[n - a])) {
                selectMin++;
            }
            int total = selectMin;
            int idx = n - a;
            while ((idx > 0) && (v[idx - 1] == v[n - a])) {
                idx--;
                total++;
            }

            long result = 0;
            if (v[n - 1] == v[n - a]) {
                for (int i = selectMin; i <= Math.min(total, selectMin + b - a); i++) {
                    // result += choose(total, i);
                    result += Combinatorics.choose(total, i).longValue();
                }
            } else {
                result += Combinatorics.choose(total, selectMin).longValue();
            }
            out.println(result);
        }

    }

    static class InputReader {
        private static BufferedReader in;
        private static StringTokenizer tok;

        public InputReader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public long[] readLongArray(int n) {
            long[] ar = new long[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nextLong();
            }
            return ar;
        }

        public String next() {
            try {
                while (tok == null || !tok.hasMoreTokens()) {
                    tok = new StringTokenizer(in.readLine());
                }
            } catch (IOException ex) {
                System.err.println("An IOException was caught :" + ex.getMessage());
            }
            return tok.nextToken();
        }

    }

    static class Combinatorics {
        long[] fact;
        long[] invFact;
        int max;
        int mod;

        public Combinatorics(int modul, int m) {
            //modul should be prime

            mod = modul;
            max = m;
            fact = new long[max];
            invFact = new long[max];
            fact[1] = 1;
            fact[0] = 1;
            invFact[1] = 1;
            invFact[0] = 1;
            for (int i = 2; i < max; i++) {
                fact[i] = fact[i - 1] * i % mod;
            }

            invFact[max - 1] = modInverse(fact[max - 1], mod);
            for (int i = max - 2; i >= 0; i--) {
                invFact[i] = ((i + 1) * invFact[i + 1]) % mod; //.. 1 / i! = (i + 1) * 1 / (i + 1)!
            }
        }

        public Combinatorics(int modul) {
            // modul should be prime

            this(modul, 3000000);
        }

        public static BigInteger choose(long n, long k) {
            if (k < 0 || k > n) return BigInteger.ZERO;
            if (k == 0 || k == n) return BigInteger.ONE;
            if (k > n - k) k = n - k;

            return choose(n - 1, k - 1).multiply(BigInteger.valueOf(n)).divide(BigInteger.valueOf(k));
        }

        public static long modPow(long a, long x, long p) {
            //calculates a^x mod p in logarithmic time.
            long res = 1;
            while (x > 0) {
                if (x % 2 != 0) {
                    res = (res * a) % p;
                }
                a = (a * a) % p;
                x /= 2;
            }
            return res;
        }

        public static long modInverse(long a, long p) {
            //calculates the modular multiplicative of a mod m.
            //(assuming p is prime).
            return modPow(a, p - 2, p);
        }

    }
}